Probability

6 )

Two dice are thrown simultaneously. What is the probability of getting the sum of the numbers as even?

1/3

2/3

1/2

3/4

None of these

View Solution

Answer :

Throw two dice n(s)=36

E is nos sum is even.

Hence E={( 1,1 ),(1,3 ) (1,5 ) (2,2 ) , (2,4 ) ,

(2,6 ),.............. ( 6,2 ), (6,4 ), ( 6,6 )}

n(E)= 18

Thus required probability= 18/36= 1/2

7 )

A basket contains 8 Red and 6 Pink toys. There is another basket which contains 7 Red and 8 Pink toys. One toy is to drawn from either of the two baskets. What is the probability of drawing a Pink toys?

101/210

85/156

75/210

120/156

None of these

View Solution

Answer :

Probability of one basket =1/2

1st Basket Pink toy probability =1/2* (6c1/14c1)

2nd Basket Pink toy probability = 1/2* (8c1/15c1)

Adding both (1/2*6/14) + (1/2*4/15) 3/14+4/15=101/210

8 )

Four persons are chosen at random from a group of 3 men, 5 women and 4 children. What is the probability of exactly two of them being men?

10/60

12/55

25/60

13/60

None of these

View Solution

Answer :

Total People = 3 + 5 + 4 = 12 n(s)=12c4

Probability of exactly two men and two from others N(e) = 3c2*9c2

P= (3c2*9c2)/12c4=>12/55

9 )

A box contains 3 balloons of 1 shape, 4 balloons of 1 shape and 5 balloons of 1 shape. Three balloons of them are drawn at random, what is the probability that all the three are of different shape?

3/44

5/22

3/11

10/22

None of these

View Solution

Answer :

Total=3+4+5=12

n(s)=12c3=220

n(e)=3c1 * 4c1 * 5c1 =60

p=60/220=3/11

10 )

12 persons are seated around a round table. What is the probability that two particular persons sit together?

2/11

4/21

8/21

6/21

None of these

View Solution

Answer :

In a circle of n different persons, the total number of arrangements possible = (n - 1)! n(S) = (12 - 1) = 11 !

Taking two persons as a unit, total persons = 11

Therefore no. of ways for these 11 persons to around the circular table = (11 - 1)! =

10!

In any unit, 2 particular person can sit in 2! ways.

Hence total number of ways that any three person can sit,

=n(E) = 10! * 2!

Therefore P (E) = probability of three persons sitting together = n(E) / n(S)

= (10! * 2!)/11! = 2/11.

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